Min-heap + greedy merging
Join Cable Reels with Less Work
01. The question
A technician must join all cable reels into one. Joining lengths a and b costs a + b units of work, and the joined reel can be used again. Return the minimum total work, not the final cable length.
Before revealing the idea, predict the result and describe what information you would need to track.
02. Worked example
Inputlengths = [4, 2, 7, 3]
Output30
- Join 2 and 3: cost 5. The reels are now 4, 5, and 7.
- Join 4 and 5: cost 9. The reels are now 7 and 9.
- Join 7 and 9: cost 16. Total work is 5 + 9 + 16 = 30, not 16.
Try your code
Define solve(data, parameter="") and return your result. Your code runs locally, not on a server.
Edit your test cases
Use 1-10 objects with data and an optional string parameter. Expected outputs are computed from the lesson. An optional expected field must be correct.
Input contract & reference code
Example data: [4,2,7,3]. Parameter: "". Numeric parameters arrive as strings; convert them with int(parameter) when needed.
The example and generated cases use the question’s exact variant. This checks behavior on a small test batch—not performance on every possible input.
Python downloads only when you run code, using compressed runtime assets. Code is not saved or uploaded. Enable JavaScript to run it.
Printed output
Five-second execution limit per batch. Standard-library Python only; additional packages and network access are unavailable. Stop ends execution without blocking the lesson.
03. The idea
Try sketching your own approach first. What would you track, and why would it work?
Reveal the idea
- Build a min-heap of all lengths.
- Repeatedly pop the two smallest lengths, add their sum to total work, and push the joined length.
- Stop when fewer than two reels remain.
04. Watch it happen
Use Step to move slowly, or Play to follow the whole trace. Change a preset or load your own input.
Input & settings
Red = current item / blue = active window or cells / green = completed work. A value docks at its actual destination; the original input stays unchanged. Positions start at 0.
Working state / what changes
Ready to begin
Enable JavaScript to step through the animation. The worked example and solution below remain readable without it.
Python / why it changes
The line behind the step
import heapq
def join_reels(lengths):
heap = list(lengths)
heapq.heapify(heap)
total = 0
while len(heap) > 1:
first = heapq.heappop(heap)
second = heapq.heappop(heap)
joined = first + second
total += joined
heapq.heappush(heap, joined)
return totalHow to use this walkthrough
Hover or focus a control for its label. Play forms the input and follows values into the working state. Step shows one change; Back and the slider restore exact snapshots. Reduced motion uses instant updates. Saved snapshots and sorted heap displays are teaching overhead, not algorithm complexity.
05. Python solution
import heapq
def join_reels(lengths):
heap = list(lengths)
heapq.heapify(heap)
total = 0
while len(heap) > 1:
first = heapq.heappop(heap)
second = heapq.heappop(heap)
joined = first + second
total += joined
heapq.heappush(heap, joined)
return total06. Cost & edge cases
- Time
- O(n log(n + 1))
- Space
- O(n)
- Zero or one reel requires no joins and returns 0.
- Lengths are positive integers; equal lengths are allowed.
- Greedy justification: a merge plan is a binary tree; place the two smallest weights as deepest siblings by exchanging larger weights, merge them, then apply the same argument to the smaller problem.